Lara Logan: Over-think things.

Jack Dorsey: Come out with a decision. I think I can be-- I can be silent at some times which unsettles people a bit, because they don't know what I'm thinking. The biggest thing I've learned is that I need to communicate more. I need to be more vocal.

Not communicating well created problems for him at Twitter. And Jack Dorsey, like Steve Jobs, was forced out of running the company he helped found.

Lara Logan: Were you angry?

Jack Dorsey: Yeah. I was angry. I was angry at-- you know, the board. I was angry at my co-founders. I was angry at myself.

Lara Logan: You once described it as being like a punch in the guts.

Jack Dorsey: Yeah.

Logan: No grudges? You don't hold any grudges?

Jack Dorsey: I'm stubborn but I don't necessarily hold grudges.

Two and a half years later, new management at Twitter invited him back to help run the company. And Dorsey accepted. Suddenly he had two jobs. By then he had dreamed up a new company, Square, that he believes can also change the world. And he says he runs it differently than Twitter. Decisions made behind closed doors are sent out immediately on the company's mass email system including sensitive information on company goals and profits. Dorsey roams around the office, available to talk to anyone.

Lara Logan: Do you have an office here?

Jack Dorsey: I don't. I don't have an office. I don't have a desk.

Lara Logan: You don't have a desk at all, even, like--

Jack Dorsey: I don't have a desk. I have my iPad.

While Twitter is about messages, Square is about money. It permits anyone with a smart phone to become a merchant. The concept grew out of a brainstorming session with a friend named Jim McKelvey, who was both a software ace and a frustrated artist.

Jack Dorsey: He was at an art fair and he couldn't sell a piece of glass because he couldn't accept a credit card. So, that was, you know, $2,000 lost. And he just got fed up with that. And he came out to San Francisco that next week and we spent the week trying to figure out why no one has done this before.

Lara Logan: And this, at that moment, was what?

Jack Dorsey: Well, we didn't know what it was. It was a way to accept credit cards on your phone. That's all we knew.

The software is simple and it's fast -- two qualities that are most important to Dorsey. To take a payment, you swipe a customer's credit card through a white square that plugs into the earphone jack.

Jack Dorsey: So you just take the card, you swipe it through...

The customer signs a receipt electronically. Department stores don't use it yet, but millions of small business people do.